Confidence Interval Concepts: How to Calculate and Interpret Confidence Intervals

A. If the confidence level is increased there, is a rise in the confidential interval which raises the probability of population mean being contained between the confidential intervals. 

B. On increase of population sample, it leads to deduction of errors simulating sampling distribution that’s is more clustered around the population mean 

C. Higher marginal errors simplify the inappropriate population sample. Increasing marginal error in statistics leads to the acknowledgement that the sample population used is inappropriate. 

16. Sample population=2303 

Believers=734 

Mean=believers population/total sample population 

=734/2303 

=0.31871477199 

Confidence interval=µ±Z*√(standard deviation/√n) 

Presuming s to be standard error given by s/√n 

=734/√2303 

=15.29498623 

C.I=0.3187±1.645√(√(15.29/2303)) 

=0.3187±0.1340 

= (0.1847, 0.4527) 

Since the confidential level lies below 50%, there are less U.S adults who believe in UFOs. The sample population mean lies in between the confidential interval but though there is a lesser probability of population mean lying in between since the confidential interval is so minimal that it is below 50%. 

18. 

a) since on the question we have not been given a preconceived idea of the sample population we use 50% since it is the most conservative giving the largest sample size calculation. 

Margin error=2% 

Sample size= Z*^2pq/M.E^2 

n=2.58^2 0.5 0.5/0.02^2 

n=1.6641/0.0004 

n=416.025 

Rounding up you get 

=417 

b) p=0.87 prior to previous investigations 

q=1-p=1-0.87=0.13 

n=2.58^2*0.87*0.13/0.02^2 

n=0.75283884/0.0004 

n=1,882.09 

38. 

Mean=150 

Total sample population=60 

Standard deviation=15.50 

Confidential level=99% 

Confidential interval=µ±Z*s.d/√n 

Where µ=sample mean 

Z*=level of confidence 

s.d=standard deviation 

n=total sample population 

n=150±2.58*(15.5/√60) 

n=150±5.163 

n= (144.837,155.163) which our confidential interval 

The sample mean of the population lies in between the confidential interval hence there is a higher possibility that the population means also lies in between since the confidential interval is over 100% (2017). 

References 

(2017). Retrieved 3 April 2017, from https://people.ucalgary.ca/~keivan.hassanimonfar/courses/Stat171F14/WS06-review.pdf